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<b>let </b><font color="Maroon" title="c1">AS</font> be   <a href="diraf.html#NM1" title="DIRAF:NM.1">AffinSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font>;<br/><b>let </b><font color="Maroon" title="c4">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">AS</font>;<br/>







<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E34">A1</font></i>: 
( <font color="Maroon" title="c4">A</font> <a href="aff_1.html#NR2" title="AFF_1:NR.2">is_line</a>  &amp; <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> )
 ;<br/>

<div><i><font color="Green" title="E35">A2</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1"/><i><font color="Green" title="E36">A3</font></i>: 
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font>
 ;<br/><b>consider </b><font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c6">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E3:37_1"/><i><font color="Green" title="E37">A4</font></i>: 
( <font color="Maroon" title="c5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q</font> &amp; <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> )
 <b>by </b><i><a class="txt" href="aff_1.html#E1:37"><i><font color="Green" title="E34">A1</font></i></a>, <a class="ref" href="aff_1.html#D3" target="_self" title="AFF_1:def.3">Def3</a></i>;<br/><a NAME="E4:37_1"/>
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="aff_1.html#E1:37"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="aff_1.html#E1:37_1"><i><font color="Green" title="E36">A3</font></i></a>, <a class="txt" href="aff_1.html#E3:37_1"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="aff_1.html#T36" target="_self" title="AFF_1:th.36">Th36</a></i>;<br/><a NAME="E5:37_1"/><b>then </b>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font>
 <b>by </b><i><a class="ref" href="aff_1.html#T13" target="_self" title="AFF_1:th.13">Th13</a></i>;<br/><b>hence </b><a NAME="E6:37_1"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="txt" href="aff_1.html#E3:37_1"><i><font color="Green" title="E37">A4</font></i></a>, <a class="ref" href="aff_1.html#D4" target="_self" title="AFF_1:def.4">Def4</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_2"/>
<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">A</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c5">p</font>, <font color="Maroon" title="c6">q</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">AS</font><b> such that </b><br/><a NAME="E3:37_2"/><i><font color="Green" title="E36">A5</font></i>: 
( <font color="Maroon" title="c5">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">q</font> &amp; <font color="Maroon" title="c4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aff_1.html#K2" title="AFF_1:func.2">Line</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> &amp; <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> )
 <b>by </b><i><a class="ref" href="aff_1.html#D4" target="_self" title="AFF_1:def.4">Def4</a></i>;<br/><a NAME="E4:37_2"/>
<font color="Maroon" title="c5">p</font>,<font color="Maroon" title="c6">q</font> <a href="analoaf.html#R2" title="ANALOAF:pred.2">//</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font>
 <b>by </b><i><a class="txt" href="aff_1.html#E3:37_2"><i><font color="Green" title="E36">A5</font></i></a>, <a class="ref" href="aff_1.html#T13" target="_self" title="AFF_1:th.13">Th13</a></i>;<br/><b>hence </b><a NAME="E5:37_2"/>
<font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font>
 <b>by </b><i><a class="txt" href="aff_1.html#E1:37"><i><font color="Green" title="E34">A1</font></i></a>, <a class="txt" href="aff_1.html#E3:37_2"><i><font color="Green" title="E36">A5</font></i></a>, <a class="ref" href="aff_1.html#T36" target="_self" title="AFF_1:th.36">Th36</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:37"/>
( <font color="Maroon" title="c3">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">A</font> iff <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">b</font> <a href="aff_1.html#R2" title="AFF_1:pred.2">//</a> <font color="Maroon" title="c4">A</font> )
 <b>by </b><i><a class="txt" href="aff_1.html#E2:37"><i><font color="Green" title="E35">A2</font></i></a></i>;<br/>


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